Given vectors a = 2i + 3j + 6k and b = Zi + j + 2k

Now, if a and b are parallel, then a*b = 0

=> |i  j  k|

     |2 3 6| = 0

     |z 1  2|

=> i(3*2 - 6) - j(2*2 - 6z) + k(2*1 - 3z) = 0

=> i(6 - 6) - j(4 - 6z) + k(2 - 3z) = 0

=> i(6 - 6) + j(6z - 4) + k(2 - 3z) = 0

=> 6z - 4 = 0 or 2 - 3z = 0

=> z = 4/6 or 3z = 2

=> z = 2/3